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Gorenstein n-余挠模及Gorenstein n-余挠维数

黄俊红 张翠萍

黄俊红, 张翠萍. Gorenstein n-余挠模及Gorenstein n-余挠维数[J]. 华南师范大学学报(自然科学版), 2015, 47(6): 111-115.
引用本文: 黄俊红, 张翠萍. Gorenstein n-余挠模及Gorenstein n-余挠维数[J]. 华南师范大学学报(自然科学版), 2015, 47(6): 111-115.
Gorenstein n-Cotorsion Modules And Gorenstein n-Cotorsion Dimension[J]. Journal of South China normal University (Natural Science Edition), 2015, 47(6): 111-115.
Citation: Gorenstein n-Cotorsion Modules And Gorenstein n-Cotorsion Dimension[J]. Journal of South China normal University (Natural Science Edition), 2015, 47(6): 111-115.

Gorenstein n-余挠模及Gorenstein n-余挠维数

基金项目: 

国家自然科学基金项目

详细信息
    通讯作者:

    黄俊红

Gorenstein n-Cotorsion Modules And Gorenstein n-Cotorsion Dimension

Funds: 

The National Natural Science Foundation of China

  • 摘要: 设 R 是环,M是左R-模,n是一个固定的非负整数.称M是Gorenstein n-余挠的,如果对任意Gorenstein n-平坦左R-模N,有Ext_{R}^{1}(N,M)=0.本文主要在右n-凝聚环上讨论了Gorenstein n-余挠模及模和环的Gorenstein n-余挠维数的相关性质.
  • [1] BENNIS D. Rings over which the class of Gorenstein flat modules is closed under extensions[J].Comm. Algebra, 2009, 37:855-868 [2]YANG Gang, LIU Zhongkui.Gorenstein flat covers over GF-closed rings[J].Comm. Algebra, 2012, 40(5):1632-1642 [3] MAO Lixin, DING Nanqing.The cotorsion dimension of modules and rings 2006, 249 : 217-233[J].Abelian Groups, Rings, Modules, and Homological Algebra, 2006, 249:217-233 [4]GAO Zenghui.On Gorenstein cotorsion dimension over GF-closed rings[J].Bull. Korean Math. Soc., 2014, 51(1):173-187 [5]LEE S B.n-coherent rings[J].Comm. Algebra, 2002, 30(3):1119-1126 [6] SELVARAJ C, UDHAYAKUMAR R, UMAMAHESWARAN A.Gorenstein n-flat modules and their covers[J].Asia-European Journal of Mathematics, 2014, 7(3):- [7] ENOCHS E E, JENDA O M G.Relative homological algebra[M]. Belin : Walter de Gruyter, 2000. [8] DING Nanqing.On envelopes with the Unique Mapping Property[J]. [J].Comm. Algebra, 1996, 24:1459-1470 [9]ENOCHS E E, JENDA O M G, LOPEZ-RAMOS J A.The existence of Gorenstein flat covers[J].Math. Scand, 2004, 94(1):46-62 [10] HOIM H.Gorenstein homological dimensions[J]. [J].Journal of Pure Application Algebra, 2004, 189:167-193 [11] 佟文廷.同调代数引论[M].北京:高等教育出版社, 1998.

    [1] BENNIS D. Rings over which the class of Gorenstein flat modules is closed under extensions[J].Comm. Algebra, 2009, 37:855-868 [2]YANG Gang, LIU Zhongkui.Gorenstein flat covers over GF-closed rings[J].Comm. Algebra, 2012, 40(5):1632-1642 [3] MAO Lixin, DING Nanqing.The cotorsion dimension of modules and rings 2006, 249 : 217-233[J].Abelian Groups, Rings, Modules, and Homological Algebra, 2006, 249:217-233 [4]GAO Zenghui.On Gorenstein cotorsion dimension over GF-closed rings[J].Bull. Korean Math. Soc., 2014, 51(1):173-187 [5]LEE S B.n-coherent rings[J].Comm. Algebra, 2002, 30(3):1119-1126 [6] SELVARAJ C, UDHAYAKUMAR R, UMAMAHESWARAN A.Gorenstein n-flat modules and their covers[J].Asia-European Journal of Mathematics, 2014, 7(3):- [7] ENOCHS E E, JENDA O M G.Relative homological algebra[M]. Belin : Walter de Gruyter, 2000. [8] DING Nanqing.On envelopes with the Unique Mapping Property[J]. [J].Comm. Algebra, 1996, 24:1459-1470 [9]ENOCHS E E, JENDA O M G, LOPEZ-RAMOS J A.The existence of Gorenstein flat covers[J].Math. Scand, 2004, 94(1):46-62 [10] HOIM H.Gorenstein homological dimensions[J]. [J].Journal of Pure Application Algebra, 2004, 189:167-193 [11] 佟文廷.同调代数引论[M].北京:高等教育出版社, 1998.
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出版历程
  • 收稿日期:  2015-03-16
  • 修回日期:  2015-04-27
  • 刊出日期:  2015-11-25

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